Séminaire interne GREDEG - Michela Chessa

Séminaire interne GREDEG

Michela Chessa

Abstract: After Parliament elections, the situation when different parties have to decide which coalitions to join to create the governing majority is quite standard on the political podium. On the one hand, in order to choose between the different alternatives, a party needs a tool to evaluate correctly its actual position and its bargaining power under the different majorities. On the other hand, the same tool may be used by an external agent to predict which coalition is the most likely to form the majority. Two factors are fundamental for developing a correct voting model. Firstly, the party's social impact, reflected in the effective number of seats that the party won during the elections (weights). Secondly, the party's ability to cooperate with other parties and that may be represented in terms of possible communication links between parties (network structure).

In this paper we introduce weighted and restricted versions of the Deegan-Packel power index and provide their axiomatic characterizations. We show that the classical Deegan-Packel index, its weighted version, and its restricted version in case when restrictions are introduced by means of the communication graph, coincide correspondingly with the Shapley value, weighted Shapley value, and the Myerson value of some particular game determined by the set of minimal winning coalitions. The conditions under which the weighted Deegan-Packel power index is monotonic with respect to the players’ weights are introduced. The computations done for three real-life examples from realm of politics: (i) 1983 Italian Parliament elections after which Bettino Craxi, the leader of the Italian Socialist Party that got only 73 seats in the Lower Chamber from the total amount of 630, but that had very strong central position, became the Prime Minister; (ii) 2009 Basque Country Parliament elections after which the Basque Nationalist Party winning the largest number of seats finally was not included into the government coalition due to its weak communication ability on the political spectrum; (iii) , Israeli Knesset election 2009 after which the Prime Minister Benjamin Netanyahu was chosen not from the winning party Kodima, but from the next winning Likud due to its better ability to cooperate with other parties, clearly demonstrate the coincidence of our theoretical predictions with the reality.